Abstract: Tsallis' non-extensive entropy is used as a regularization operator. The parameter "q" (non-extensivity parameter) has a central role in the Tsallis' thermostatiscs formalism. Here, several values of q are investigated in an inverse problem, using q<1 and q>1. Two standard regularization techniques are recovered for special q-values: (i) q=2 is the well known Tikhonov regularization; (ii) q=1 is the standard Boltzmann-Gibbs-Shannon formulation for entropy. The regularization feature is illustrated in an inverse test problem: the estimation of initial condition in heat conduction problem. Two methods are studied for determining the regularization parameter, the maximum curvature for the $L$-curve, and the Morozov's discrepancy principle. The new regularization of higher order is applied to the retrieval of the atmospheric vertical profile from satellite data.